The position of an object as a function of time is given as

Question

x = At3 + Bt2 + Ct + D.
The constants are
A = 3.2 m/s3,
B = 1.8 m/s2,
C = −4.2 m/s,
and
D = 7 m.

At what time(s) is the object at rest?

Answer 1

It is at rest when the derivative dX/dt = 0

So solve
9.6t^2 +3.6t -4.2 = 0
which is the same as
16t^2 +6t -7 = 0
This can be factored to give
(2t -1)(8t+7) = 0

They probably want only the solution for which t>0.

Answer 2

2.1